Core losses: Quantification and electronic structure - PowerPoint PPT Presentation

Core losses: Quantification and electronic structure FYS5310/FYS9320 Lecture 6 23.02.2016

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Elemental quantification • The core loss EELS edges can be used to quantify the composition of your specimen • In particular useful for low-Z elements 3

The fluorescence yield in EDS analysis The probability for generating a characteristic X-ray is given by the fluorescence yield w The probability of generating an Auger electron is the 1- w. Very few X-ray generated F&H

Elemental quantification • The core loss EELS edges can be used to quantify the composition of your specimen • In particular useful for low-Z elements • You also avoid some of the experimental errors of EDS 5

Spurious and system X-rays in EDS analysis • Spurious X-rays from the specimen, but not the region of interest • System X-rays from the sample holder, specimen support grid, microscope itself (Cu, Fe) W&C

Elemental quantification • The core loss EELS edges can be used to quantify the composition of your specimen • In particular useful for low-Z elements • You also avoid some of the experimental errors of EDS (spurious and system X-rays) • In the first approximation, the observed intensity I of edge i of element A is: 𝑗 = 𝐽 0 𝑂 𝑗 𝐽 𝐵 𝐵 𝜏 𝐵 • Relative composition is then 𝑘 𝑗 𝑂 = 𝐽 𝐵 𝜏 𝐶 𝐵 𝑗 𝑘 𝑂 𝐶 𝜏 𝐽 𝐶 𝐵 7

Boron K edge Nitrogen K edge 8

What scattering cross section do we use?  1  2 9

What scattering cross section do we use? Sample  Collection angle To prism 10

What scattering cross section do we use? • In practice, our experiment looks only at inelastic scattering in an energy range [E,E+  ] and scattering angle [0,  ] Partial cross section  (  ,  ) must be used • 11

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Geometry of the experiment Incident beam convergence angle  Microscope in Collection angle determined by imaging mode size of microscope objective apperture diffraction mode size of spectrometer entrance apperture Sample  GIF entrance apperture or Microscope objective apperture Collection angle 13 To prism

How to determine partial cross sections • Calculations – Hydrogenic model – Hartree-Slater model • Experimentally 14

Background removal Power law model: 15

Plural scattering • Remove using Fourier-ratio or Fourier-log methods 16

Free atom cross sections compared to spectra from materials 17

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Under usual assumtions, the core loss EELS spectrum probes the • local density of states around the excited atom… • with symmetry l  1… • above the Fermi-level The site and symmetry selected DOS 19

L 2 L 3 20

L 2 L 3 21

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The 3d orbitals 23

Let’s imagine octahedral coordination 24

Ti 3d orbitals 25

e g t 2g e g t 2g L 2 L 3 26

Direct comparison with calculated density of states (DOS) • The transition matrix determines the underlying edge shape • Usually slowly varying with energy • The density of states gives more rapid variations on top of this • Allows comparison with calculated DOS, e.g. from density functional theory (DFT)

Direct observations of charge transfer in copper oxide Cu 2+ O 2− Charge is transferred from copper atom towards oxygen because of + O 2− Cu 2 greater electronegativity Cu metal V. J. Keast et al. J. Microsc. (2001)

Oxygen 2p DOS of AlV 2 O 4

The core hole problem • We have so far assumed that the probed DOS is the ground state DOS • But we are explicitly exciting the system out of the ground state E F • Coloumb interaction between electron and hole Change in electrostatic potential  change • in the DOS and rearrangement of charge

The core hole problem SiO 2 as an example p  s,d Si L 2,3 Experiment s and d DOS with core hole s and d ground state DOS • The core hole should in principle always be accounted for s  p O K • Neglecting the core hole sometimes works well or even better (metals), other p ground state DOS times not (insulators and Experiment oxides) J. B. Neaton et al . Phys. Rev. Lett. (2000)

• If the initial states are sharply peaked in energy, then all transitions originate at this energy • One particular E i and one particular E takes you to a single point in the conduction band E f • In effect we are convoluting the conduction band DOS with a delta function 𝐸𝑓𝑚𝑢𝑏 𝑔𝑣𝑜𝑑𝑢𝑗𝑝𝑜 ⊗ 𝑑𝐸𝑃𝑇 = 𝑑𝐸𝑃𝑇 • But what if the initial states are in the valence band? 𝑤𝐸𝑃𝑇 ⊗ 𝑑𝐸𝑃𝑇 =? • Topic for next time 32